Federal Reserve Bank of New York
Economic September 2008 September Volume 14 Number 2 14 Number Volume Policy Review
Special Issue: The Economics of Payments ECONOMIC POLICY REVIEW
EDITOR Kenneth D. Garbade
COEDITORS Mary Amiti Adam B. Ashcraft Robert W. Rich Asani Sarkar
EDITORIAL STAF F Valerie LaPorte Mike De Mott Michelle Bailer Karen Carter
PRODUCTION STAFF Carol Perlmutter David Rosenberg Jane Urry
The Economic Policy Review is published by the Research and Statistics Group of the Federal Reserve Bank of New York. Articles undergo a comprehensive refereeing process prior to their acceptance in the Review. The views expressed are those of the individual authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. www.newyorkfed.org/research Federal Reserve Bank of New York Economic Policy Review
September 2008 Volume 14 Number 2
Special Issue: The Economics of Payments
Contents
3Introduction James McAndrews
Theoretical Models of Money and Payments Articles:
7 Intraday Liquidity Management: A Tale of Games Banks Play Morten L. Bech
Over the last few decades, most central banks, concerned about settlement risks inherent in payment netting systems, have implemented real-time gross settlement (RTGS) systems. Although RTGS systems can significantly reduce settlement risk, they require greater liquidity to smooth nonsynchronized payment flows. Thus, central banks typically provide intraday credit to member banks, either as collateralized credit or priced credit. Because intraday credit is costly for banks, how intraday liquidity is managed has become a competitive parameter in commercial banking and a policy concern of central banks. This article uses a game-theoretical framework to analyze the intraday liquidity management behavior of banks in an RTGS setting. The games played by banks depend on the intraday credit policy of the central bank and encompass two well-known paradigms in game theory: “the prisoner's dilemma” and “the stag hunt.” The former strategy arises in a collateralized credit regime, where banks have an incentive to delay payments if intraday credit is expensive, an outcome that is socially inefficient. The latter strategy occurs in a priced credit regime, where postponement of payments can be socially efficient under certain circumstances. The author also discusses how several extensions of the framework affect the results, such as settlement risk, incomplete information, heterogeneity, and repeated play. 25 An Economic Analysis of Liquidity-Saving Mechanisms Antoine Martin and James McAndrews
A recent innovation in large-value payments systems has been the design and implementation of liquidity-saving mechanisms (LSMs), tools used in conjunction with real-time gross settlement (RTGS) systems. LSMs give system participants, such as banks, an option not offered by RTGS alone: they can queue their outgoing payments. Queued payments are released if some prespecified event occurs. LSMs can reduce the amount of central bank balances necessary to operate a payments system as well as quicken settlement. This article analyzes the performance of RTGS systems with and without the addition of an LSM. The authors find that, in terms of settling payments early, these mechanisms typically outperform pure RTGS systems. However, there are times when RTGS systems can be preferable to LSMs, such as when many banks that send payments early in RTGS choose to queue their payments when an LSM is available. The authors also show that the design of a liquidity-saving mechanism has important implications for the welfare of system participants, even in the absence of payment netting. In particular, the parameters specified determine whether the addition of an LSM increases or decreases welfare.
41 Divorcing Money from Monetary Policy Todd Keister, Antoine Martin, and James McAndrews
Many central banks implement monetary policy in a way that maintains a tight link between the stock of money and the short-term interest rate. In particular, their implementation procedures require that the supply of reserve balances be set precisely in order to implement the target interest rate. Because bank reserves play other key roles in the economy, this link can create tensions with other important objectives, especially in times of acute market stress. This article considers an alternative approach to monetary policy implementation—known as a “floor system”—that can reduce or even eliminate these tensions. The authors explain how this approach, in which the central bank pays interest on reserves at the target interest rate, “divorces” the supply of money from the conduct of monetary policy. The quantity of bank reserves can then be set according to the payment or liquidity needs of financial markets. By removing the opportunity cost of holding reserves, the floor system also encourages the efficient allocation of resources in the economy. Empirical Analyses of Trends in Large-Value Payments Articles:
59 Global Trends in Large-Value Payments Morten L. Bech, Christine Preisig, and Kimmo Soramäki
Globalization and technological innovation are two major forces affecting the financial system and its infrastructure. Perhaps nowhere are these trends more apparent than in the internationalization and automation of payments. While the effects of globalization and technological innovation are most obvious on retail payments, the influence is equally impressive on wholesale, or interbank, payments. Given the importance of payments and settlement systems to the smooth operation and resiliency of the financial system, it is important to understand the potential consequences of these developments. This article presents ten major long-range trends in the settlement of large-value payments worldwide. The trends are driven by technological innovation, structural changes in banking, and the evolution of central bank policies. The authors observe that banks, to balance risks and costs more effectively, are increasingly making large-value payments in real-time systems with advanced liquidity-management and liquidity-saving mechanisms. Moreover, banks are settling a larger number of foreign currencies directly in their home country by using offshore systems and settling a greater number of foreign exchange transactions in Continuous Linked Settlement Bank or through payment-versus-payment mechanisms in other systems. The study also shows that the service level of systems is improving, through enhancements such as longer operating hours and standardized risk management practices that adhere to common standards, while transaction fees are decreasing. Payments settled in large-value payments systems are more numerous, but on average of smaller value. Furthermore, the overall nominal total value of large-value payments is increasing, although the real value is declining.
83 Changes in the Timing Distribution of Fedwire Funds Transfers Olivier Armantier, Jeffrey Arnold, and James McAndrews
The Federal Reserve’s Fedwire funds transfer service—the biggest large-value payments system in the United States—has long displayed a peak of activity in the late afternoon. Theory suggests that the concentration of late-afternoon Fedwire activity reflects coordination among participating banks to reduce liquidity costs, delay costs, and credit risk; as these costs and risk change over time, payment timing most likely will be affected. This article seeks to quantify how the changing environment in which Fedwire operates has affected the timing of payment value transferred within the system between 1998 and 2006. It finds that the peak of the timing distribution has become more concentrated, has shifted to later in the day, and has actually divided into two peaks. The authors suggest that these trends can be explained by a rise in the value of payments transferred over Fedwire, the settlement patterns of the private settlement institutions that use the system, and an increase in industry concentration. Although the study’s results provide no specific evidence of heightened operational risk attributable to activity occurring later in the day, they point to a high level of interaction between Fedwire and private settlement institutions. 113 The Timing and Funding of CHAPS Sterling Payments Christopher Becher, Marco Galbiati, and Merxe Tudela
Real-time gross settlement (RTGS) systems such as CHAPS Sterling require large amounts of liquidity to support payment activity. To meet their liquidity needs, RTGS participants borrow from the central bank or rely on incoming payments from other participants. Both options can prove costly—the latter in particular if participants delay outgoing payments until incoming ones arrive. This article presents an empirical analysis of the timing and funding of payments in CHAPS. The authors seek to identify the factors driving the intraday profile of payment activity and the extent to which incoming funds are used as a funding source, a process known as liquidity recycling. They show that the level of liquidity recycling in CHAPS is high and stable throughout the day, and attribute this result to several features of the system. First, the settlement of time- critical payments provides liquidity to the system early in the settlement day; this liquidity can be recycled for the funding of less urgent payments. Second, CHAPS throughput guidelines provide a centralized coordination mechanism, in effect limiting any tendency toward payment delay. Third, the relatively small direct membership of CHAPS facilitates coordination between members, for example, through the use of bilateral net sender limits. Coordination encourages banks to maintain a relatively constant flux of payments throughout the day. The authors also argue that the high level of recycling helps to reduce liquidity risk, and that the relatively smooth intraday distribution of payments serves to mitigate operational risk associated with highly concentrated payment activity. They note, however, that the benefits of liquidity recycling are not evenly distributed between members of CHAPS.
Risk Management in Payments Systems Articles:
137 Understanding Risk Management in Emerging Retail Payments Michele Braun, James McAndrews, William Roberds, and Richard Sullivan
New technologies used in payment methods can reduce risk, but they can also lead to new risks. Emerging retail payments are prone to operational and fraud risks, especially security breaches and potential use in illicit transactions. This article describes an economic framework for understanding risk control in retail payments. Risk control is a special type of good because it can protect one payment participant without diminishing the protection of other participants. As a result, the authors’ economic framework emphasizes risk containment, primarily through the establishment and enforcement of risk management policies. Application of the framework to three types of emerging payments suggests that a payments system can successfully manage risk if it quickly recognizes problems, encourages commitment from all participants to control risk, and uses an appropriate mix of market and public policy mechanisms to align risk management incentives. The authors conclude that providers of emerging payment methods must mitigate risk effectively or face rejection in the payment market. 161 An Economic Perspective on the Enforcement of Credit Arrangements: The Case of Daylight Overdrafts in Fedwire Antoine Martin and David C. Mills
A fundamental concern for any lender is credit risk—the risk that a borrower will fail to fully repay a loan as expected. Thus, lenders want credit arrangements that are designed to compensate them for—and help them effectively manage—this type of risk. In certain situations, central banks engage in credit arrangements as lenders to banks, so they must manage their exposure to credit risk. This article discusses how the Federal Reserve manages its credit risk exposure associated with daylight overdrafts. The authors first present a simple economic framework for thinking about the causes of credit risk and the possible tools that lenders have to help them manage it. They then apply this framework to the Federal Reserve’s Payments System Risk policy, which specifies the use of a variety of tools to manage credit risk. The study also analyzes a possible increase in the use of collateral as a credit risk management tool, as presented in a recent proposal by the Federal Reserve concerning changes to the Payments System Risk policy.
Introduction
James McAndrews
James McAndrews
Introduction
imply put, payments settle things. A payment is typically theoretically and empirically; risk in retail payments systems; S the final step in a sequence of activities that make up an payments system development trends across countries; and the economic or financial trade. Because the parties to the trade interaction of the provision of reserves by central banks and the look forward to this final step, payments are the focus of their operation of payments systems. They illustrate the diversity of expectations about timing, risks, and costs. The more certain it interests and methods that economists have developed for is that this final step of a trade will take place, the easier it is for studying payment activities. trades to occur and for people to undertake efficient economic The contributions to this volume center on three broad actions. themes: theoretical models of money and payments, empirical As the world economy continues to grow, the share devoted analyses of trends in large-value payments, and risk to financial services has risen relative to the share representing management in payments systems. other economic activities. Payments have increased in The theoretical theme is examined in three articles—by importance as that trend has manifested itself, and their Morten L. Bech; Antoine Martin and James McAndrews; and contribution to the global economy is likely to increase as well. Todd Keister, Antoine Martin, and James McAndrews. The The rising importance of payments to economic activity in Bech study and the Martin-McAndrews study, both focusing general is a significant development—especially for banks and on large-value payments systems, explore the strategic central banks as providers of payment services. Bank customers incentives for banks to submit payments on time in different frequently rely on credit provided by their institutions to economic environments. They consider how the incentives are complete payments, whether they are using credit cards or affected by different central bank policies, such as the terms other payment instruments. Similarly, banks often rely on under which intraday credit is provided. Keister, Martin, and very-short-term credit provided by central banks to make McAndrews consider alternative models of monetary policy payments. Needless to say, whenever financial institutions implementation as well as the relationship between the provide credit, they must manage risk to prevent excessive risk demand for intraday balances to meet payment needs and the taking. Managing payments is therefore part of a larger risk reserve balances used to implement the policy objectives of the management process in the financial sector. monetary authorities. This special issue of the Economic Policy Review is devoted to Bringing an empirical perspective to the topic, Morten L. the economics of payments. The wide-ranging articles in this Bech, Christine Preisig, and Kimmo Soramäki conduct a global collection investigate large-value payments systems, both tour of developments in large-value payments over the last
James McAndrews is a senior vice president at the Federal Reserve Bank The views expressed are those of the author and do not necessarily reflect of New York. the position of the Federal Reserve Bank of New York or the Federal
FRBNY Economic Policy Review / September 2008 3 decade. Relying largely on data compiled by the Bank for Two studies consider the theme of risk management—one International Settlements, the authors discern a number of key by Michele Braun, James McAndrews, William Roberds, and trends in the growth and evolution of large-value payments. Richard Sullivan, the other by Antoine Martin and David C. In addition, two articles focusing on the timing of large-value Mills. Both apply the economic reasoning associated with risks payments systems—the first by Olivier Armantier, Jeffrey in credit arrangements to the specific case of payments. Braun Arnold, and James McAndrews and the second by Christopher et al. emphasize emerging retail systems while Martin and Mills Becher, Marco Galbiati, and Merxe Tudela—complement focus on the risk associated with a central bank’s intraday Bech’s theoretical work by explaining how different central lending to banks. bank policies influence payment timing. Both empirical The economics of payments is a rapidly developing field. analyses use data obtained directly from the large-value These studies offer a variety of approaches that use theoretical payments systems they study. Armantier, Arnold, and as well as empirical techniques to explore different aspects McAndrews review the timing distribution of payments of payments. Going forward, as researchers gain greater access in Fedwire, the Federal Reserve’s system, while Becher, to payment data, they will be better equipped to test other Galbiati, and Tudela consider the timing of payments in hypotheses about the determinants of behavior in payments CHAPS, the major U.K. system. The differences in timing systems. We hope that our findings will stimulate such between the two systems are found to be significant. initiatives and deepen interest in this dynamic field.
4 Introduction Theoretical Models of Money and Payments
Articles by:
Morten L. Bech Antoine Martin and James McAndrews Todd Keister, Antoine Martin, and James McAndrews
Morten L. Bech
Intraday Liquidity Management: A Tale of Games Banks Play
• To ensure smooth operation of real-time 1. Introduction gross settlement systems, central banks extend intraday credit, either against “[Banks] like to hang on to their cash and deliver it collateral or for a fee. as late as possible at the end of the working day.” “The Long Shadow of Herstatt,” The Economist, • As intraday credit is costly—either explicitly April 14, 2001 as fees or implicitly as the opportunity cost of collateral—participating banks seek to The value and volume of interbank payments increased minimize their use of liquidity by timing the dramatically throughout the 1980s and 1990s as a result of rapid release of payments. financial innovation and the integration and globalization of financial markets. In the United States, settlement of interbank payments grew from $300 trillion in 1985, or forty-five times • A game-theoretical study of intraday liquidity GDP, to almost $500 trillion in 1995, or seventy-five times GDP management behavior shows how the (Bech, Preisig, and Soramäki 2008). strategic incentives of banks depend on the Historically, interbank payments have been settled via intraday credit policy of central banks. deferred (end-of-day) netting systems. As the volume and value of transactions increased, however, central banks became • Two classic games emerge: “the prisoner’s worried about settlement risks inherent in netting systems. In dilemma” and “the stag hunt.” particular, the banks were concerned about the potential for contagion, or “knock-on,” effects attributable to the • The prisoner’s dilemma arises in a unwinding of net positions that would result if a participant collateralized credit scenario, where banks failed to meet its end-of-day obligations. Consequently, over delay payments even though they would be the last couple of decades, many countries have chosen to better off if they all sent payments early; the modify the settlement procedures employed by their interbank stag hunt arises in a priced credit scenario, payments system. where banks seek to coordinate the timing Most central banks opted for the implementation of a real- of their payments to avoid overdraft fees. time gross settlement (RTGS) system. By 1985, three central
Morten L. Bech is a senior economist at the Federal Reserve Bank of New York. The views expressed are those of the author and do not necessarily reflect the
FRBNY Economic Policy Review / September 2008 7 banks had implemented RTGS systems. A decade later, that different intraday credit policy regimes employed by central number had increased to sixteen, and at the end of 2006 the use banks. We characterize how the Nash equilibria depend on of RTGS systems had diffused to ninety-three central banks the underlying cost parameters, and discuss the efficiency (Bech and Hobijn 2007). implications of the different outcomes. As it turns out, two RTGS systems eliminate the settlement risk from unwinding classic paradigms in game theory emerge from the analysis: the because payments are settled irrevocably, and with finality, on “prisoner’s dilemma” and the “stag hunt.” Hence, many policy an individual gross basis and in real time. However, the questions can be understood in terms of well-known conflicts elimination of settlement risk comes at the cost of an increased and dilemmas in economics. This study uses the framework to need for liquidity to smooth nonsynchronized payment flows.1 conduct a comparative analysis of the relative desirability of Thus, central banks typically provide intraday credit. different intraday credit regimes from the perspective of a Two types of intraday credit policies have emerged among benevolent central bank. In addition, it discusses in turn how central banks: collateralized credit and priced credit (Furfine several extensions of the model will affect the results. These and Stehm 1998). Collateralized credit, in one form or another, extensions include settlement risk, incomplete information, is the prevailing option in Europe and elsewhere outside the heterogeneity, repeated play, multitudes of players, and more than just two actions. We conclude with general observations on the future of intraday liquidity management. This article develops a stylized game- theoretical model to analyze banks’ intraday liquidity management behavior 2. Intraday Liquidity Management in an RTGS [real-time gross settlement] Game
environment. Envision an economy with two identical banks using an RTGS system operated by the central bank to settle interbank claims.2 Bank A and Bank B seek to minimize the cost of making their United States. Collateralized credit usually takes the form of payments. We look at one business day that consists of two pledging collateral to the central bank or entering into an periods: morning and afternoon. intraday repurchase agreement with the central bank. Priced At dawn, both banks receive a request from a customer to credit is the policy of choice in the United States. The Federal pay $1 to a customer of the other bank on the same business Reserve has been charging a fee for intraday overdrafts since day.3 Assume for simplicity that the banks can either process 1994. Quantitative limits, or “caps,” are used in combination the request right away, or postpone it until the afternoon with both types of credit extensions. period. We abstract from reserve requirements and Intraday credit is costly, whether explicitly in the form of a fee precautionary motives for banks to hold balances with the or implicitly as the opportunity cost of the pledged collateral. central bank, and thus each bank has a zero balance on its Consequently, banks try to economize on their use of liquidity settlement account at dawn. Banks cannot send payments from throughout the day by carefully scheduling the settlement of their accounts in amounts that exceed their account balances. payment requests received from customers and the banks’ own However, banks can borrow funds from the central bank. The proprietary operations. Intraday liquidity management has cost of borrowing and how it is assessed depend on the intraday become an important competitive parameter in commercial credit policy of the central bank. Here, overdrafts are assessed banking and a policy concern of central banks (see, for example, at noon and at the end of the day. Overnight overdrafts are Greenspan [1996] and Berger, Hancock, and Marquardt [1996]). penalized at a very high rate, making banks avoid them This article develops a stylized game-theoretical model to altogether. analyze banks’ intraday liquidity management behavior in an If there were no adverse consequences, each bank would RTGS environment. It analyzes the strategic incentives under prefer to postpone making its payment and use the funds received via incoming payments from the other bank to 1 In most RTGS systems, payments are settled using reserve account balances at the central bank. For an individual bank, there are basically four different provide the balances to cover its own outgoing payments. sources of liquidity to fund outgoing payments: 1) overnight reserve balances, 2 In many countries, the interbank payments systems are neither owned nor 2) intraday credit extensions by the central bank, 3) borrowing from other operated by the central bank, but rather by a private company or a consortium banks via the interbank money market, and 4) incoming payments from other of banks. However, payments are usually settled in liabilities on the central banks. The first two sources affect the aggregate level of liquidity available in the bank. For ease of exposition, we ignore these differences here. system, while the latter two redistribute the liquidity among banks. Moreover, 3 liquidity from the first three sources generally comes at a price, whereas liquidity The customer could be internal to the bank, in which case the decision- from incoming payments is free from the perspective of the receiver. making agent can be thought of as the payment manager of the bank.
8 A Tale of Games Banks Play Game 1 Game 2 Intraday Liquidity Management Game Free Intraday Credit Game
Bank B Bank B morning afternoon morning afternoon morning 0, 0 0, D morning cA(m,m), cB(m,m) cA(m,a), cB(a,m) Bank A Bank A afternoon D, 0 D, D afternoon cA(a,m), cB(m,a) cA(a,a), cB(a,a) Note: We underline the cost associated with the strategy that is the best response of a bank given the strategy played by the other.
However, postponing is also costly, as customers might either demand compensation for late settlement or take their business outcomes by comparing both individual and aggregate elsewhere in the future, thereby imposing a reputation cost on settlement costs. The regimes are free, collateralized, or priced the delaying bank. intraday credit. For many payments, the cost of intraday delay is presumably small, as the underlying contractual obligation of the customer only specifies payment on a given business day. However, for an increasing number of financial transactions, the underlying contract stipulates payment prior to some 3. Free Intraday Credit Regime specific time on a given business day, and the cost of delay The first adopters of RTGS systems provided intraday credit could conceivably be high. Here, we simply assume the cost of for free, and we use this intraday credit policy regime as a delay to be a positive number D per dollar per period within.4 benchmark. With free credit within the day, there is no Moreover, postponing payments until the next day is extremely incentive to postpone payments. The free intraday credit game expensive in terms of reputation effects or direct compensation is shown in Game 2. to customers, so banks always submit any remaining payments It is best for both banks to play the morning strategy because in the afternoon. they incur no costs. Conversely, they incur the cost of delay if A convenient way of arranging the possible actions of the they postpone to the afternoon. The morning strategy banks and the associated costs is a 2 x 2 game, as shown in dominates the afternoon strategy, and the strategy profile Game 1. Each bank can play one of two strategies: morning or (morning, morning) is said to be an equilibrium in dominating afternoon. The first element in each cell denotes the settlement strategies. A pair of dominating strategies is a unique Nash cost of Bank A, whereas the second element denotes that of equilibrium. Bank B. Following Bech and Garratt (2003), we label this game In Game 2 and in other games, we adopt the convention of the intraday liquidity management game. underlining the cost associated with the strategy that is the best In the next three sections, we explore the games that emerge response of a bank given the strategy played by the other. We under different intraday credit regimes. Our solution concept summarize the results of the free intraday credit game in Result 1: is Nash equilibrium—that is, a set of strategies for which neither bank would wish to change its strategy on the Result 1: Early settlement (morning, morning) is a unique assumption that the other bank will not change its strategy equilibrium in the free intraday credit game. The outcome is either. We focus on Nash equilibria in pure strategies—that is, efficient in that it ensures the lowest possible aggregate strategies where a player chooses to take one action with settlement cost across all pairs of strategies. probability 1—which is in contrast to a mixed strategy, where individual players choose a probability distribution over In reality, payment flows are not perfectly symmetric as they several actions. We evaluate the efficiency of different are in the model, and imbalances frequently occur. Moreover, the zero price for intraday credit creates no incentives to 4 Delay has several private and social costs associated with it. First, time is economize on overdrafts.5 In fact, the size of the overdrafts money (even intraday) and hence delay of settlement may displease customers and counterparties, which are left with higher costs and greater uncertainty. generated by banks (relative to their capital base) in an RTGS Second, delayed settlement increases operational risk insofar as the time span environment came as a surprise to many central banks. As during which an incident may disrupt the settlement process increases and the guarantor of the finality of payments, the central bank is time to recover after an incident decreases. Third, the process of delaying can be costly, and the resources devoted to managing intraday positions are a cost. exposed to credit risk—as, ultimately, are taxpayers. Hence, Fourth, delay increases the length of time participants may be faced with credit central banks are almost unanimous in the opinion that the risk exposures vis-à-vis each other. provision of free intraday liquidity is not a viable option.6
FRBNY Economic Policy Review / September 2008 9 4. Collateralized Intraday Credit Game 3 Regime Collateralized Credit Game Bank B In most countries, central banks provide commercial banks morning afternoon with intraday credit against collateral. The practical morning C, C 2C, D Bank A implementation varies across countries, depending on the afternoon D, 2C C + D, C + D institutional infrastructure for the safekeeping and settlement of securities. For ease of exposition, we assume that credit is extended via intraday repurchase agreements (repos), as in the United Kingdom and Switzerland. the cost of delaying is greater than the cost of obtaining Under the intraday repo agreement, the central bank liquidity—that is, D > C—then banks have no incentive to provides the bank with $1 in its account at the beginning of the delay and the strategy profile (morning, morning) is the only period in return for eligible collateral worth the same amount Nash equilibrium. If Bank B plays morning, the best strategy plus a “haircut” to cover any market and credit risk associated for Bank A is to play morning as well. Moreover, if Bank B with the collateral. At the end of the period, the transaction chooses to postpone, the best strategy for Bank A is still is reversed. The central bank does not charge explicit interest morning. In other words, morning is a dominating strategy for this service, but the collateral subject to repo entails an for Bank A and, by symmetry, for Bank B as well. However, opportunity cost for the banks, as this collateral cannot be used if the cost of liquidity is higher than the cost of delaying— for other purposes. The opportunity cost of collateral is that is, C > D—then the strategy profile (afternoon, assumed to be C per period per dollar. afternoon) is the only Nash equilibrium. It is a unique Nash If Bank A and Bank B both decide to process their requests equilibrium, since neither bank wishes to switch to morning early, then they each have to engage in an intraday repo with if the other bank keeps playing afternoon because a switch the central bank in order to obtain liquidity, and consequently would increase its settlement cost. However, it is also clear they will each incur the cost C. However, if, say, Bank A decides that the banks would be better off if they both chose to to delay while Bank B decides to process, then Bank A will incur process payments in the morning. Unfortunately, (morning, the cost of delay D in the morning period. However, in the morning) is not an equilibrium in this one-shot game. afternoon period, it can use the incoming liquidity from Bank Starting from (morning, morning), each bank would wish to B to fund its own outgoing payment in the next period. postpone payment in order to lower its settlement cost. This Conversely, Bank B receives no liquidity and has to roll over the strategic situation is a classic paradigm in game theory called repo with the central bank for an additional period and incur the prisoner’s dilemma.7 We summarize the results of the the cost C one more time for a total of 2C. Finally, if both banks collateralized credit game in Result 2: choose to postpone, they both incur the cost of delay D. Result 2: In the collateralized credit game, early settlement Moreover, at noon they still have no liquidity available, and (morning, morning) is a unique equilibrium if the both have to engage in an intraday repo in the afternoon period opportunity cost of collateral is less than the cost of delaying for which they each will incur the opportunity cost of collateral C. The settlement costs are summarized in Game 3, hereafter 7 The “prisoner’s dilemma” is the most famous paradigm in game theory. referred to as the collateralized credit game. Suppose that the police have arrested two former felons who they know have In the collateralized credit game, the equilibrium committed an armed robbery together. Unfortunately, they lack enough admissible evidence to get a jury to convict them of armed robbery. They do, depends solely on the relative size of the opportunity cost of however, have enough evidence to send each prisoner away for two years for collateral and the cost of postponing a payment request. If theft of the getaway car. Prisoner’s Dilemma 5 In 2006, the Federal Reserve eliminated the extension of free intraday credit to government-sponsored enterprises (GSEs) and certain international Prisoner 2 organizations for the purpose of securities-related interest and redemption Confess Silence Confess 5, 5 0, 10 payments. This action was taken in part because, for some issuers, the lag Prisoner 1 between the time the Federal Reserve credited the interest and redemption Silence 10, 0 2, 2 payments to the recipients’ accounts (early in the morning) and the time the issuer covered the resulting overdraft extended, at times, until shortly before The chief inspector now makes the following offer to each prisoner: “If you will the close of the Fedwire system, hence exposing the Federal Reserve to credit confess to the robbery, implicating your partner, and he does not also confess, risk for the duration of the day. Currently, interest and redemption payments then you’ll go free and he will get ten years. If you both confess, you’ll each get have to be funded up front. five years. If neither of you confesses, then you’ll each get two years for the auto 6 In models without credit risk, Freeman (1996) and Martin (2004) find that theft.” It is a Nash equilibrium for each prisoner to confess; yet they would both free intraday credit is the socially optimal policy. be better off if they both chose to remain silent.
10 A Tale of Games Banks Play Chart 1 Game 4 Pricing Structure for Swiss Interbank Clearing Offsetting in the Morning Game (C > D) CHF per payment 3.5 Bank B morning afternoon 3.0 Sender (above morning 0, 0 2C, D 100,000 CHF) Bank A afternoon D, 2CC + D, C + D 2.5 Note: We underline the cost associated with the strategy that is the best 2.0 response of a bank given the strategy played by the other. Sender (under 1.5 100,000 CHF) 1.0
0.5 Receiver Third, central banks can use pricing. For example, the Swiss 0 Before 8 a.m. 8 a.m. - 11 a.m. 11 a.m. - 2 p.m. After 2 p.m. National Bank charges higher prices for payments sent later in the day, thereby giving banks a direct incentive to process early. Source:
8 See Danmarks Nationalbank (2003).
FRBNY Economic Policy Review / September 2008 11
Game 5 Game 6 Priced Credit Game Priced Credit as the Stag Hunt Game
Bank B Bank B morning afternoon morning afternoon morning 0, 0 F, D morning 0, 0 5, 2 Bank A Bank A afternoon D, F D, D afternoon 2, 5 2, 2
Note: We underline the cost associated with the strategy that is the best response of a bank given the strategy played by the other.
dominates late submission, and one would expect banks to choose the cost-efficient strategy. In sum, the introduction of if both banks choose to postpone, neither bank would a gridlock-resolution mechanism may change submission unilaterally want to deviate and process because that would behavior. We offer the following conjecture: increase its settlement cost from 2 cents to 5 cents. Conjecture: Gridlock resolution and offsetting mechanisms Here, the priced credit game has the structure of a classic 9 may eliminate the potential prisoner’s dilemma. coordination game called the stag hunt. The key feature of the stag hunt game is that while the (morning, morning) The issue of liquidity-saving mechanisms is discussed equilibrium is preferred by both players in terms of lowest cost, further in Martin and McAndrews (2008). the other is preferred in terms of strategic risk. In the early- settlement equilibrium, the settlement cost of one bank depends on the action of the other. One bank’s deviation from morning, for whatever reason, will impose increased 5. Priced Intraday Credit Regime settlement costs on the other bank. In contrast, the strategy to postpone payments carries no risk in the sense that the Under the priced credit regime, banks are charged the fee F per settlement cost is the same regardless of which action the other dollar if their settlement account is overdrawn at the end of a bank takes. A cautious bank may reasonably choose to period. This implies that no overdraft fee is incurred if the postpone, ensuring the 2 cents with certainty rather than banks manage to synchronize their payments. The settlement risking the cost of 5 cents. This is especially true if there are costs associated with the different possible pairs of strategies concerns regarding the other bank’s ability to coordinate (for are shown in Game 5, the priced credit game. example, because of operational risk). We recap the results of If both banks play morning, then payments net out and the priced credit game in Result 3: banks incur no costs. The payments also net out if both banks play afternoon, but each will incur the cost of delay. If one bank Result 3: In the priced credit game, early settlement pays and the other delays, then the paying bank will incur (morning, morning) is a unique equilibrium if the an overdraft at noon while the other can use the incoming overdraft fee is less than the cost of delaying (F < D). The payment from the morning period to fund its outgoing outcome is efficient. In contrast, both (morning, morning) payment in the afternoon. However, the bank that delays will and (afternoon, afternoon) are feasible equilibria if F > D incur the cost D. and the game is a stag hunt. Late settlement is inefficient. As in the collateralized credit regime, the outcome depends In the prisoner’s dilemma, there is a conflict between on the relative size of the cost of liquidity and the cost of individual rationality and mutual benefit. In the stag hunt, postponing the processing of a request. Again, the strategy rational players are pulled in one direction by consideration of profile (morning, morning) is a unique Nash equilibrium if the mutual benefit and in the other by individual risk concerns cost of liquidity is less than the cost of delaying the payment (Skyrms 2004). In the stag hunt game, the outcome depends on request—that is, F < D. the player’s appetite for strategic risk—that is, the uncertainty However, if F > D, then the strategy profiles (morning, morning) and (afternoon, afternoon) are both Nash equilibria. To 9 The “stag hunt” is a story that became a game. The game is a prototype of the see this, assume that F = 5 cents and D = 2 cents, as in Game 6. social contract. The story is briefly told by the eighteenth-century philosopher If both banks choose to process payments early, then neither Jean-Jacques Rousseau in A Discourse on Inequality (Skyrms 2004): “If it was a matter of hunting a deer, everyone well realized that he must remain faithful to bank would want to change and postpone because that would his post; but if a hare happened to pass within reach of one of them, we cannot increase its settlement cost from 0 cents to 5 cents. Likewise, doubt that he would have gone off in pursuit of it without scruple.”
12 A Tale of Games Banks Play that arises from the interaction between the players of the Chart 2 game. The conflict in the priced credit game is a trade-off Comparative Analysis of Intraday Credit Regimes between lower settlement costs and strategic risk. Priced credit One way of pinning down a unique equilibrium is by using Harsanyi and Selten’s (1988) concept of risk dominance.10 In a F F = 2C F = C symmetric 2 x 2 game, risk dominance asserts that players will 4: 3: choose the strategy that gives the highest expected payoff under Collateralized Priced the assumption that the opponent randomizes with equal (a,a) credit credit preferred preferred probability over the two available strategies. Fixing D to be 2 cents in Game 6 implies that (morning, morning) is the risk- 2D dominant equilibrium if F < 4 cents and (afternoon, afternoon) 1: is the outcome if F > 4 cents. Priced credit preferred Result 4: In the priced credit game, the risk-dominant 2: Priced equilibrium is early settlement (morning, morning) if (m,m) credit F < 2D. Otherwise, late settlement (afternoon, afternoon) is preferred the risk-dominant equilibrium.
Using the analysis above, we now turn to a comparison of the aggregate settlement costs to the economy under 45° collateralized and priced intraday credit policy regimes. (m,m) D (a,a) C Collateralized credit
6. Choice of Intraday Credit Policy
An omnipresent question for central banks is the choice of The aggregate settlement costs under the equilibria of the intraday credit policy. For example, the Board of Governors of the two intraday credit regimes are easily calculated by summing Federal Reserve System is currently reviewing its Payment System the entries in each cell in Game 3 and Game 5, respectively. The Risk Policy with a view to reducing liquidity risk, credit risk, and aggregate settlement costs when one bank is playing morning operational risk while maintaining or improving payments system and the other afternoon are 2C + D and F + D, respectively, efficiency. For this reason, the Federal Reserve Board published under the two regimes. With two possible (risk-dominant) a consultation paper in June 2006 to elicit information from Nash equilibria under each regime, there are four different financial institutions and other interested parties on their scenarios to consider. experiences managing intraday risk associated with Fedwire funds The comparative analysis is summarized in Chart 2. The X-axis transfers. Our model can provide insight into the desirability of shows the Nash equilibrium in a collateralized credit regime different payments system policies and highlight some of the as a function of the opportunity cost of collateral. The Y-axis difficulties facing policymakers. shows the risk-dominant Nash equilibrium under a priced Assume that a central bank is a benevolent provider of the credit regime as a function of the overdraft fee. In the priced RTGS system insofar as it seeks to secure the lowest possible credit regime, aggregate settlement costs are zero if the aggregate settlement costs for the economy. The central bank equilibrium is (morning, morning). In contrast, a collateralized can choose between a collateralized credit and a priced credit credit regime always implies positive settlement costs. regime. Additionally, for the purposes of this analysis, assume Consequently, priced credit is the preferred regime if F < 2D— that the central bank cannot (further) influence the cost of that is, in scenarios 1 and 2. In other words, take the parameters liquidity under either regime or the cost of delay. The preferred of the model as exogenously given. regime then depends on the equilibrium outcome under the If payments are delayed under both regimes—that is, 2D two regimes, which in turn depends on the relative magnitudes < F and D < C—then aggregate settlement costs are 2D + 2C of F, C, and D. and 2D, respectively. Hence, priced credit is the preferred regime C in scenario 3 in Chart 2. Conversely, collateralized 10 In 1994, John C. Harsanyi and Reinhard Selten were awarded the Nobel Prize in Economics, together with John F. Nash Jr., for their pioneering analysis of credit is the preferred regime if banks do not delay payments equilibria in the theory of noncooperative games. under such a regime but they do under a priced credit
FRBNY Economic Policy Review / September 2008 13 regime—that is, C < D < 2D < F (scenario 4). We summarize 7. Settlement Risk this as: Settlement risk is an important concern in all payment Result 5: Priced credit is preferred to collateralized credit arrangements (see, for example, Kahn, McAndrews, and except when collateralized credit leads to quicker settlement Roberds [2003] and Mills and Nesmith [2008]). Fundamentally, of payments. it is the risk that settlement does not take place as expected. The model provides very clear results in terms of the As such, settlement risk comprises both liquidity and credit desirability of the two regimes, but in reality the analysis is risks. Liquidity risk is the risk that a counterparty will not settle more involved. Moreover, the analysis does not take into an obligation for full value when due, but at some unspecified account default risk, against which the collateral protects. time thereafter. Credit risk is the risk that a counterparty A challenge for comparative analysis in practice is that the cost will not settle an obligation for full value either when due or of delay is not observable. In fact, little is known about the anytime thereafter. The presence of settlement risk affects the costs banks face if they delay settlement of payments. Without strategic interaction between banks and hence their intraday knowledge of the cost of delay, the comparative analysis liquidity management behavior. becomes less informative, but the simple analysis presented in To illustrate how settlement risk affects strategic Chart 2 does yield the following necessary, but not a sufficient, interaction, we assume that the banks have entered into condition for collateralized credit to be the preferred regime: trades with each other yielding obligations to pay the other $1, to be settled gross. On settlement day, a bank might Result 6: For collateralized credit to be the preferred regime, a necessary condition is that the opportunity cost of collateral be lower than (literally half) the overdraft fee The presence of settlement risk affects the charged under priced credit. strategic interaction between banks and The opportunity cost of collateral is not directly observable hence their intraday liquidity management either, but the rate differential between federal funds loans, which are uncollateralized, and loans through repurchase agreements, behavior. which are collateralized, suggests that the opportunity cost is in the range of 12 to 15 basis points per annum (see Board of Governors experience an operational incident or default altogether, of the Federal Reserve System [2006]).11 However, the overdraft which leads to either a temporary inability or permanent fee is readily observable because it is set by the central bank with failure to pay. Because payment flows are symmetric, a view to managing credit exposure from overdrafts. Currently, neither bank starts out with an exposure vis-à-vis the other daylight overdraft fees in the Fedwire Funds Service are calculated at dawn. If a bank defaults before the opening of the RTGS using an annual rate of 36 basis points, quoted on the basis of a system, the other bank can just withhold its payment. 21.5-hour day. This simple “back-of-the-envelope” comparison However, by paying early, a bank exposes itself to the suggests that there may be scope for investigating an increased inability or failure of the other to pay. Everything else being role for collateral in the Fedwire system. equal, one would expect banks to be more cautious in their In the following sections, we investigate how the conclusions behavior when facing settlement risk. In essence, settlement from the model are likely to change as more realism is added. We risk reduces the effective cost of delaying. start by considering settlement risk, followed by incomplete Specifically, we model liquidity risk by assuming that, with information, repeated play, and more than two banks and periods. probability ω, banks will not be able to submit payments to the In Box 1 and Box 2, we analyze, respectively, the strategic RTGS system in the morning because of, say, a telecommuni- interaction between banks when there is no intraday credit cations outage. However, the telecommunications links to available and when banks are heterogeneous. stricken banks are reestablished at noon and banks can then make payments in the afternoon period. The expected costs for banks are derived in the appendix. These costs are used in the intraday liquidity management games with liquidity risk shown in Game 7 and Game 8 for the two policy regimes (collateralized credit and priced credit). For convenience, we 11 The opportunity cost of collateral would, in all likelihood, increase if the Federal Reserve implemented a collateralized credit regime because the show only the costs for Bank A, but by symmetry the costs are demand for collateral would increase. the same for Bank B.
14 A Tale of Games Banks Play Box 1 The No Intraday Credit Game
The exception proving the rule that early adopters provided than the cost of delay, the game is an anti-coordination game, so intraday credit for free is Switzerland. The Swiss National Bank named because it is mutually beneficial for the players to play implemented real-time gross settlement (RTGS) systems in 1987, different strategies. If Bank B plays morning, then the best response but did not provide intraday credit until the autumn of 1999. The of Bank A is to play afternoon. Conversely, if Bank B plays change in policy was motivated by an increase in time-critical afternoon, then the best strategy for Bank A is to play morning. The payments and, in particular, the future introduction of the underlying conflict in the game is that both banks want to benefit Continuous Linked Settlement system for foreign exchange from free liquidity, but liquidity is rivalrous—that is, banks cannot transactions. According to Heller, Nellen, and Sturm (2000), benefit from it at the same time. Hence, both (morning, afternoon) the amount of payments settled by noon rose from one-third and (afternoon, morning) are possible Nash equilibria, but neither to one-half of the daily turnover as a result. Pareto dominates the other or is focal in any sense. The mixed- Going against conventional wisdom, the Reserve Bank of strategy Nash equilibrium implies that banks play morning with New Zealand implemented a new liquidity management regime in probability pD= ⁄ ρ and afternoon with the complementary 2006 that discontinued its intraday automatic reverse repurchase probability. The expected settlement cost for a bank is ρ (see facility (autorepo). Instead, the Reserve Bank chose to supply a appendix). Hence, the mixed strategy does not Pareto dominate significantly higher level of cash (overnight monies) sufficient to either of the pure Nash equilibria, and a bank might as well play enable participants to settle payments efficiently. The change was morning and save itself the trouble of randomizing. necessitated by a growing scarcity of New Zealand government It is not obvious how banks can solve the conundrum of who securities (see Reserve Bank of New Zealand [2006]). gets the benefit of free liquidity. One solution in these types of If the central bank does not provide intraday credit, then games is for banks to engage in pre-play communication. In pre- payments have to be funded by balances held with the central bank, play communication, each player announces the action it intends interbank money market borrowings, or incoming payments from to take (or, alternatively, the action it would like the other to take). other banks. The first two sources are costly, whereas the last is free In game theory, pre-play communication that carries no cost is from the perspective of the receiver. Let ρ denote the (marginal) referred to as cheap talk (Farrell and Rabin 1996). Interestingly, opportunity cost of balances held at the central bank. The in some experimental settings, cheap talk has been found to be opportunity cost of reserves is closely linked to the central bank’s effective. Another form of pre-play communication is for one bank policy with respect to remunerating reserves. If the central bank to signal convincingly that it will play afternoon. One way to do does not pay interest on reserves, then the opportunity cost is close this would be to open late, but that would probably be bad for to the overnight money market rate, whereas if the central bank business in general and thus costly. does pay interest on reserves, it depends on the difference between Aumann (1974) provides a generalization of Nash equilibrium the money market rate and the administrative rate paid on known as correlated equilibrium, which allows for possible reserves. dependencies in strategic choices. A perfectly correlated The no intraday credit game is given below for the interesting equilibrium would be for banks to use a fair coin to determine case where ρ > D . which bank gets to play afternoon. In a repeated setting, a convention for banks to alternate sending early could conceivably No Intraday Credit Game ( > D) evolve. Above and beyond the potential instability of the equilibrium Bank B outcome, a key insight of the no intraday liquidity management morning afternoon game is that the monetary policy stance may directly affect the morning , , D Bank A afternoon D, D + , D + settlement of payments intraday owing to the close link between the opportunity cost of holding reserves and the overnight interest Note: We underline the cost associated with the strategy that is the rate. Any movement in the monetary policy stance will affect the best response of a bank given the strategy played by the other. opportunity cost and may shift the equilibrium around. Interestingly, Heller, Nellen, and Sturm (2000) claim that a less If the opportunity cost of reserve balances is less than the cost restrictive monetary policy stance from 1993 to 1999 can explain a of delay, then (morning, morning) is the equilibrium in dominating large part of the reduced congestion observed in Swiss Interbank strategies. However, if the opportunity cost of reserves is larger Clearing, as this led banks to hold increased account balances.
FRBNY Economic Policy Review / September 2008 15 Box 2 Heterogeneity
In the analysis, we focus on the interaction between two identical loan late is a weakly dominating strategy because if the issuer for banks. Obviously, participants in a real-time gross settlement some reason should delay then it would be best for the bank to system are not a homogenous group. Here, we explore the delay as well. A small intraday opportunity cost for a bank using implications of introducing heterogeneity among participants. For overdraft capacity to cover the interest on the loan would eliminate ease of exposition, we consider only two cases. First, we look at the the (morning, morning) equilibrium. The (morning, afternoon) case where participants face different liquidity and delay costs. We equilibrium leaves the issuer with an overdraft at the central bank do this in the context of a recent policy change in the Fedwire for the entire day. In sum, different cost structures for participants system. Second, we consider the case where payment flows are not can lead to interesting games with asymmetric equilibria. We now balanced and then we try to gauge the extent to which that affects turn to payment flow imbalances. the strategic interaction between banks. On any given day, payment flows are never balanced because In 2006, the Federal Reserve eliminated the extension of free banks receive different amounts of payment requests from their intraday credit to government-sponsored enterprises (GSEs) and customers. Banks manage their projected end-of-day balances certain international organizations for the purpose of securities- throughout the day. Liquidity is redistributed via the interbank related principal and interest payments. This action was taken in part money market from the “haves” to the “have nots.” The question because, for some issuers, the lag between the time the Federal is the extent to which such differences in payment flows can affect Reserve credited the interest and redemption payments to the the strategic interaction among banks. To provide insight, we recipients’ accounts (early in the morning) and the time the issuer assume that Bank B has two $1 payments to send to Bank A covered the resulting overdraft extended, at times, until shortly whereas Bank A still has only $1 to send to Bank B. The strategy set before the close of the Fedwire system. As a result, the Federal expands for Bank B, which can choose to send them both early, Reserve was exposed to credit risk for the duration of the day. delay them both, or send one early while holding back the other. Currently, principal and interest payments have to be funded up The resulting games are shown below. front. To see how the simple framework can account for this Collateralized Credit Game with Payment Flow observation, assume that one player is now an issuer of securities Imbalance (C > D ) and needs to pay $1 in principal and interest to the other player— a bank. Assume that issuer had the necessary cash to pay out Bank B principal and interest on hand the previous day and chose to lend m,m m,a a,a mC, 3CC, D+2C 2C, 2D+C it out in the overnight money market to earn a return. For Bank A simplicity, also assume that the borrower was the bank that aD, 4CD, D+3CD+C,2D+2C henceforth has to return the $1 plus interest ()ρ to the issuer. Note: We underline the cost associated with the strategy that is the The central bank is granting free intraday credit to the issuer best response of a bank given the strategy played by the other. but charges the bank for overdrafts. Owing to market conventions, the cost of delaying the payout of principal and interest is high (H), The games become slightly more complicated, but the whereas the cost of delaying the return of a money market loan to fundamental issues remain. In the case of collateralized credit, a participant that has access to free intraday credit is virtually nil. banks may still end up delaying payments even though it is more The resulting principal and interest game is shown below. efficient to process early in terms of minimizing aggregate settlement cost. In the case of priced credit, it is possible only to offset two payments against each other, and thus it turns out that Principal and Interest Game Bank B will always hold back one payment. The stag hunt is played with the remaining payment. Issuer morning afternoon Priced Credit Game with Payment Flow morning F, 0 (1+ )F, H Bank afternoon F, 0 F, H Imbalance ( F > D )
Note: We underline the cost associated with the strategy that is the Bank B best response of a bank given the strategy played by the other. m,m m,a a,a m 0, 2F 0, D+F F, F+2D Bank A Clearly, it is a dominating strategy for the issuer to pay out aD, 3FD, D+2FD, 2D+F early. If the issuer plays morning, then the bank is indifferent Note: We underline the cost associated with the strategy that is the between returning early or late. However, returning the overnight best response of a bank given the strategy played by the other.
16 A Tale of Games Banks Play Game 7 Exhibit 2 Collateralized Credit Game with Liquidity Risk Equilibrium and Efficiency in the Priced Credit Game with Liquidity Risk Bank B morning afternoon (a, a)(m,m), (a, a)(m,m) morning (1+ )C+ D 2C+ D Bank A afternoon D+ CD+C efficient stag hunt efficient